A good way to improve your posture without having to commit any time to going to the gym or any other regular exercise routine is to find posture exercises you can do while you are at work or while you are stuck in traffic during your commute.
Most days when I drive home from work I am in stand still traffic for at least 20 minutes. I have found several exercises that I can perform while I am waiting. One of the simplest ones is to simply lower your chin onto your chest while keeping your back and shoulders straight and motionless.
Once you get your chin down, push it down as if you are trying to make it reach your stomach, but don't move you shoulders or bend your back. If you do this for five seconds or so and do it say 10 times then that is a good workout. You can find other simple exercises like this one and develop an entire routine that you can perform during your day, and you don't have to make any changes to your schedule.